Outer boundary of the expanding cosmos: Discrete fields and

1

Outer boundary of the expanding cosmos:

Discrete fields and implications for the

holographic principle

Pons D.J.,1 Pons A.D.

Abstract

A physical interpretation of the holographic principle is derived, using a

specific non-local hidden-variable theory called the Cordus conjecture. We

start by developing an explanation for the vacuum, and differentiate this

from the void into which the universe expands. In this theory the vacuum

comprises a fabric of discrete field elements generated by matter

particules. The outside void into which the universe expands is identified as

lacking a fabric, and also being without time. From this perspective the

cosmological boundary is therefore the expanding surface where the fabric

colonises the void. Thus the cosmological boundary is proposed to contain

the discrete field elements of all the primal particules within the universe,

and therefore contains information about the attributes of those

particules at genesis. Inner shells then code for the changed locations of

those particules and any new, or annihilated, particules. Regarding the

notion of holographic control of inner contents of the universe from the

outer surface, this theory identifies the infeasibility of placing a physical

Agent at the boundary of the universe, and also predicts there is no

practical way to control the universe from its outer boundary as the

holographic principle suggests. It also rejects the notion that the boundary

contains information about the future and past, or about all possible

universes. The Cordus model suggests that there is no causality from the

boundary of the universe to its inner contents.

Date: Monday, 4 March 2013 > Document: Pons_Cordus_CM-07-03_Frontier_E5_29.doc

Keywords: cosmological horizon; holographic principle; cordus conjecture; observer;

contextual measurement; non-local hidden-variable solution; vacuum; time; atemporal;

interaction; fundamental physics; pre-spacetime;

1 Introduction

The holographic principle is that the information content of all the matter

that has fallen into a black hole can be represented by fluctuations in the

surface of the event horizon [1]. Extending this to the universe as a whole,

the principle suggests that the two-dimensional (2-D) information on the

outside surface of the universe, the cosmological boundary, encodes for

the whole three-dimensional (3-D) content of the universe within [2-3].

The concept is typically identified with string theory [2] and information

1 Please address correspondence to Dr Dirk Pons, Department of Mechanical

Engineering, University of Canterbury, Private Bag 4800, Christchurch 8020, New

Zealand, Email: [email protected]. Copyright D Pons, AD Pons 2013.

This work is made available under the Creative Commons Attribution-Non-

Commercial-ShareAlike 3.0 license.

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theory [4]. The holographic principle implies that everything that we

perceive as physical and real in the universe, even life, is merely a

hologram projected in from the cosmological boundary. The true reality

would be on that 2-D surface on the edge of the universe. This concept

has significant philosophical implications for what we construe as reality.

In the present context the term ‘cosmological boundary’ refers to the

physical extent of the entire universe, not merely that component visible

to us. The latter is the observable universe or particle horizon, sometimes

rather confusingly referred to as the cosmological horizon. However we

use the term cosmos to refer to the entire universe, whether or not this is

observable.

In this paper we show that it is possible to provide a physical

interpretation of the holographic principle using a specific non-local

hidden-variable theory called the Cordus conjecture. We start by

developing an explanation for the vacuum. The second stage is to explain

how the cosmological boundary concept works within this framework. We

also include considerations of the observable universe. We then close by

discussing the implications.

2 The vacuum problem

There is no universally accepted interpretation of the composition of the

vacuum or explanation of its mechanics. Electromagnetic (EM) wave

theory models the vacuum as consisting of nothing at all, but yet

paradoxically having finite electric and magnetic constants. The existence

of these constants (which are presumed to be universally constant) and

the fine-structure constant alpha, is difficult to explain from within

classical EM theory. Nor is it possible from EM theory to explain why the

constants take the values they do.

Another concept for the vacuum is available in General Relativity (GR),

which includes a space-time medium [5]. It describes gravitation well,

but not the structure of matter or the other forces. It also does not

describe the composition of space-time. Furthermore it assume space-

time is smooth, which makes for difficulties integrating this concept with

other theories.

The main theory for the composition of the vacuum is undoubtedly

quantum mechanics (QM). According to the Standard model, the vacuum

contains virtual-particles, which are short-lived transient particles that are

believed to exist temporarily due to the Heisenberg uncertainty principle,

and which cannot be observed – though they are believed to be the

carrier for interactions (forces) and a variety of particle decay processes.

According to quantum field theory the vacuum state |0> contains no

physical matter, but is the ground state (zero average energy) of the

quantised electromagnetic field, for which the photon is the gauge boson

in the Standard Model. Generally the vacuum state has, by definition, zero

usable energy. However it still has vacuum fluctuations, and thus it has

zero-point energy, since its variance is not zero even if the mean is. This is

believed to be the explanation for a non-zero cosmological constant.

Quantum electrodynamics (QED) [6], models the vacuum as consisting of

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temporary energetic particles, but no average substance. These are

proposed to come in and out of existence via a pair-production >

annihilation process. The presence of the temporary particles thus give

substance to the vacuum. The corollary is that the vacuum is never empty,

even in the ground state. QM therefore does not differentiate between a

region within the universe that is current free of such particles, and a

region outside and beyond the current expansion limits of the universe.

Coupled with this, QM has no model for time; at least not one that scales

to the macroscopic level, though loop quantum gravity pursues that

goal.2

While these diverse concepts for the vacuum are individually adequate for

their respective physics, the overall situation is ontologically problematic.

For one, the existing theories conflict in their explanations. The integration

is poor, the mismatch over gravitation being a case in point. Also, these

theories find the idea of a matter-based aether unacceptable, yet ironically

all include something that looks conceptually much like a medium.

None of these theories describe what it is that the universe is expanding

into. For the sake of discussion, call that outer region the void.

Conventional physics has no way of differentiating the vacuum/void

concepts, and consequently tends to a single interpretation of vacuum

that is applied to both regions. If these are the same thing then there is an

issue of how the same vacuum that fills a finite universe, also extends to

the region beyond the universe, and whether that outer region is infinite

or bounded in some further way. However, if the vacuum and void are not

the same, then how to differentiate them?

3 Purpose

There is a need to better understand what the vacuum is within the

universe, what it is that the universe expands into, and whether the

holographic principle is a valid concept. The primary purpose of this paper

is to attempt to explain the vacuum and cosmological frontier effects,

through the lens of the Cordus conjecture. This is worth doing for the

potential to add new perspectives to the debate on this important

cosmological subject. In this specific area it provides, as will be shown,

novel explanations for the vacuum and holographic principle.

A secondary purpose is to test the logic of the conjecture. Does it have

sufficient conceptual coherence to withstand an extension of its principles

to the area under examination, or does it reduce to absurdity?3

2 Loop quantum gravity is based on a network of loops (hence the name) that

quantise geometry and are represented mathematically in a ‘spin foam’. In the

Cordus conjecture use is also made of the term ‘fabric’, but the idea is something

quite different as it refers instead to a network of interconnected discrete field

elements, and is given a physical rather than mathematical meaning. The Cordus

concept of fabric also provides for the interconnectedness of space (c.f. the

relativity of simultaneity) and thus a discrete model for both time and gravitation. 3 It is difficult for theories developed for fundamental physics to scale up to the

cosmological level. This is evident in the difficulty achieving a gravitation theory

from quantum mechanics. Likewise the de Broglie Bohm hidden-variable solution

4

The Cordus conjecture is a non-local hidden-variable (NLHV) solution [7].

The core ideas are that every particule has two reactive ends, which are a

small finite distance apart (span), and each behave like a particle in their

interaction with the external environment. A fibril joins the reactive ends

and is a persistent and dynamic structure but does not interact with

matter. Each reactive end of the particule is energised in turn at the

frequency of that particule (which is dependent on its energy). It emits a

discrete force element when it is energised. These pulses are connected in

a flux line called a hyperfine-fibril (hyff) that is emitted into the external

environment. Each reactive end of the particule emits three such

orthogonal hyff, at least in the near-field. These directions are termed

hyperfine-fibril emission directions (HEDs). The aggregation of hyff from

multiple particules creates a discrete field. The discrete force element is a

3-D composite structure. The direct lineal effect of the discrete force

element provides the electrostatic interaction, the bending of the hyff

provides magnetism, the torsion provides gravitation interaction, and the

synchronicity between discrete force elements of neighbouring particules

provides the strong force. These are all carried simultaneously by the

discrete force element as it propagates outwards on the hyff flux. See

Appendix A for a fuller description.

4 Approach

The Cordus conjecture was created with a systems design methodology,

i.e. we anticipate a set of internal and field structures for particules¸

sufficient to explain the observed functionality (physical phenomena). We

continue this logical approach.

First we determine the composition of the vacuum under the assumptions

of the Cordus conjecture. This composition we call the fabric [8], and we

propose it contains discrete fields. From this we infer the composition of

the void beyond the universe, by negation of the vacuum contents. It

helps that we have separately developed a model for time [9] within the

same Cordus theory: this is useful because it shows that time too is an

emergent property of the fabric. We infer that a region that has no fabric,

i.e. the void, is also timeless. We then show that the cosmological

boundary can be given a physical explanation in terms of the Cordus

differentiation between the vacuum within the universe and the void into

which it expands. From this are extracted implications for the holographic

principle.

We represent this theory as a causal model, using the systems

engineering modelling notation of integration definition zero (IDEF0)

[10].4 The IDEF0 model represents the proposed relationships of causality,

has little to say at the cosmological level. We are therefore interested in testing

the Cordus conjecture at this level, and seeing if it has anything meaningful to

contribute to the debate at the cosmological level. 4Legend: With IDEF0 the object types are inputs, controls, outputs, and

mechanisms (ICOM) and are distinguished by placement relative to the box, with

inputs always entering on the left, controls above, outputs on the right, and

mechanisms below.

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and thus serves the same purpose as mathematical formalism does in

conventional physics.

Any particular assumptions required, are noted as lemmas in Appendix B.

The lemmas represent the proposed Cordus mechanics, and are a

mechanism to ensure logical consistency within the wider theory.

5 Results: A cosmological boundary to the vacuum

The Cordus conjecture is a non-local hidden-variable (NLHV) solution [7].

The core ideas are that every particule has two reactive ends, which are a


interaction with the external environment. A fibril joins the reactive ends

and is a persistent and dynamic structure but does not interact with

matter. Each reactive end of the particule is energised in turn at the

frequency of that particule (which is dependent on its energy). It emits a

discrete force element when it is energised. These pulses are connected in

a flux line called a hyperfine-fibril (hyff) that is emitted into the external

environment. Each reactive end of the particule emits three such

orthogonal hyff, at least in the near-field. These directions are termed

hyperfine-fibril emission directions (HEDs). The aggregation of hyff from

multiple particules creates a discrete field. The discrete force element is a

3-D composite structure. The direct lineal effect of the discrete force

element provides the electrostatic interaction, the bending of the hyff

provides magnetism, the torsion provides gravitation interaction, and the

synchronicity between discrete force elements of neighbouring particules

provides the strong force. These are all carried simultaneously by the

discrete force element as it propagates outwards on the hyff flux. See

Appendix A for a fuller description.

5.1 System model

A cosmological framework

We start the explanation with an overview model, shown in Figure 1 (CM-

07). This provides the wider context in which to understand the boundary

effect. This is necessary because the cosmological boundary is part of a

broader set of cosmological processes. This part of the model is

represented in IDEF0 system modelling notation and should be

understood as a set of proposed causal relationships. At this level we

identify several main activities.

The first is a set of genesis production processes (1), whereby a pair of

photons are converted into the first atoms. This is followed by a rapid

expansion (2), which is the inflation of the universe. In the Cordus theory,

the inflation is driven by repulsion between the particules, in turn because

of the synchronous Interaction (strong force) [11].5 The inflation results in

5 The Cordus theory for the strong force proposes that it is a synchronous

interaction between discrete fields, as opposed to the conventional interpretation

that the force changes its nature with distance to become attractive-repulsive

(doi:http://vixra.org/abs/1208.0030). Thus in the Cordus model the synchronous

interaction prescribes displacements to pull the particules together at one

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an expanding universe, where the matter content of universe moves

outward. Those matter particules generates discrete fields (3), the

aggregation of which creates a fabric (4). The combination of fabric and

expansion creates the cosmological boundary (6).

Figure 1: The cosmological boundary is explained within the broader

Cordus cosmological theory, which is represented by this system model.

Genesis production sequence

More details about the genesis production sequence are shown in Figure

2 (CM-07-01). It involves Pair Production (1) to produce electrons,

Asymmetrical baryogenesis (2) to produce protons, Beta+ decay (3) to

produce neutrons. Hence provision of all the subcomponents for the

assembly to simple atoms (4). This represents the sequence as it is

commonly accepted, and is not in contention. However the details of

several stages in the process are incompletely understood in modern

physics. In particular the mechanics whereby photons convert to an

reactive end (or push them apart). Specifically, it is proposed that inflation arises

from a competition for field emission directions that cannot be satisfied under the

extreme constraints at genesis, so the reactive ends of the particules escape by

reenergising at more distal locations, hence outward velocity. The synchronous

interaction has a short range, hence limiting the scope of the inflation.

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electron and positron (pair production) are uncertain, and the

asymmetrical baryogenesis process is completely unknown, likewise the

asymmetrical leptogenesis. Where the Cordus theory is different is in

providing an integrated solution to all these sub-problems. Specifically,

there are detailed Cordus explanations for the mechanics of pair

production and asymmetrical genesis [12], the nucleon decay processes

[13-14], and the strong interaction [11] for assembling the atom. The

Cordus theory for the cosmological boundary is consistent with these

proposed underlying mechanics.

Figure 2: The Cordus genesis production sequence (CM-07-01).

Of relevance to what comes later is the prediction of specific roles for the

neutrino and antineutrino in the genesis sequence. The existence of

neutrinos from β+ decay is a known fact, which is accommodated and its

mechanisms further explained in the Cordus theory [15]. The Cordus

theory predicts the antineutrinos are waste products of the

remanufacturing process at asymmetrical genesis, and have a crucial role

in that process. They are also important in the later explanations for the

boundary.

5.2 Formation of the fabric

The next part of the theory describes the fabric, and how it is formed. This

has important implications for the differentiation between the vacuum

and the void.

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The fabric comprises a skein of discrete field elements, which are

generated by all the particules in the accessible universe. The way this

arises is briefly described, with reference to the system model in Figure 3.

First, the individual particules generate discrete fields (1). These interact

with the reactive ends of other particules in the electro-magnetic-

gravitational-synchronous (EMGS) interactions (2). These displacements

of reactive ends are proposed for what we more commonly perceive as

force. Fields (3) result as an aggregation of the individual discrete field

elements. The Cordus theory suggests that that discrete fields are not

consumed or changed in these interactions (4) (in contrast to the colour

change of QCD or the virtual bosons of QED), but instead continue to

propagate away from their basal particule. At the same time, the basal

particule continues to emit more discrete fields (5) each time its reactive

ends energise. The overall result is that the space between matter

particules is filled with these discrete field elements (6), and this is the

Cordus fabric.

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Figure 3: The Cordus fabric (CM-07-03).

It is worth noting that in this Cordus fabric theory, the photon needs the

fabric to propagate, due to its particular type of discrete field

arrangements [16]. In contrast the hyff from fermions are not dependent

on pre-existence of the fabric, but instead make the fabric, and are able

to propagate even in the absence of other discrete fields. This becomes

relevant when considering the cosmological frontier. Thus the vacuum

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within the bounds of the universe contains a fabric of discrete fields, and

the density thereof depends on the local abundance of matter.

Note also that the Cordus fabric is relativistic, in that for an isotropic

fabric the propagation speed of the photon is the same in any direction,

regardless of the motion of the body emitting the photon. Thus the

Cordus theory supports relativity in this aspect. The Cordus theory also

predicts that the speed of light depends on the fabric density, being

slower in more dense regions. This also explains the electric and magnetic

constants, and gives a physical interpretation of the fine structure

constant α as a measure of the transmission efficacy of the fabric [8].

While the Cordus fabric concept is similar to the space-time of general

relativity [5], there are important differences. In the Cordus theory the

fabric is discrete and therefore only approximately smooth and

continuous. Nor does the Cordus fabric carry a time dimension, though it

does have an important role in the Cordus theory for time and the

coordination underpinning the relativity of simultaneity [9].

Vacuum vs. Void

The Cordus theory of the fabric readily permits a definition of the

vacuum, and that of the void into which the universe expands.

� Vacuum: that part of the universe and its surrounds that have a non-

zero fabric density.

� Void: that region beyond the outer boundary of the cosmos, and is

characterised by having neither fabric nor time.

Cordus thus distinguishes between the fabric that makes up the vacuum

of space, as opposed to the void beyond the universe. The next stage in

the logical development of this subject is to consider the behaviour of the

outer boundary of the universe as it expands into the void.

5.3 Cosmological boundary forms

The model now is that the universe forms a fabric (vacuum), and as the

universe expands outwards so the fabric colonises the void. This is

represented diagrammatically in Figure 4. As a consequence of the

progressive nature of the genesis production sequence, and its

subsequent quiescence, a shell structure is predicted to develop for the

universe. The outer boundary of this is the cosmological boundary, and

represents the expanding interface between vacuum and void. The prime

candidates for composition of the boundary are the antineutrinos that

Cordus suggests are produced as a by-product of asymmetrical genesis

[12], and the discrete forces from those particules and the matter baryons

and leptons within the universe. We tentatively assume a propagation

mechanism: that the discrete forces that make up the fabric propagate

outwards along the hyff flux in increments of one span-length (of the base

particule) at each frequency cycle.

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Figure 4: The cosmological boundary (CM-07-06) forms as an expansion of

the universe into the void.

Shell structure

So, from the cordus perspective, the cosmological boundary of the

universe contains the discrete fields of only the primal particules within

the universe. These represent the classical electro-magnetic-gravitational

(EMG) fields. A shell structure emerges, with intermediate shells

containing discrete fields from later epochs of the universe, see Figure 5.

During these later epochs the original particules will generally have moved

to new locations, and this information is carried out by the hyff at the

local speed of light, and therefore reaches outer shells much later. In

addition, particules that are created ex photons long after the start of the

universe, e.g. via pair production, will only start emitting discrete fields

from their moment of creation, and propagate them out at the speed of

light. Therefore their discrete fields will not be represented at the

cosmological boundary, but only on inner shells. Furthermore, any one

intermediate shell contains discrete fields from a range of epochs, since

the spatial spread of matter ensures that some bodies are closer and

others further from any one point on the shell. In the limit this reduces to

an observable universe, i.e. a volume of space which has had sufficient

time to send its discrete fields to the location under examination.

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Figure 5: The Cordus model for the boundary of the cosmos. At the outer

frontier the expanding universe colonises the void. This boundary only

codes for the very first fields created at the genesis event. Inner shells code

for the later states of the universe.

The Cordus boundary is therefore broadly consistent with the

cosmological boundary and holographic principle of string theory. Both

agree that the properties on the boundary code for matter on the inside.

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6 Discussion

6.1 Comparison of the models

Despite the similarities, the Cordus theory identifies additional

characteristics of the boundary that make it different to the holographic

construct.

First, the Cordus interpretation is that the coding is only for the particules

as they once were, not for their present position within the universe nor

even for their existence. If they have subsequently been annihilated their

hyff (discrete flux lines) collapse outward only at the speed of light. Thus

Cordus predicts that the boundary will not be an up-to-date

representation of the state of the universe. It is a hologram, a 3D picture,

but one of the deep past.

Second, Cordus predicts that particules emit their discrete fields in a

directional manner, the hyff emission directions, and therefore any one

particule within the universe will display its fields at only specific locations

on the boundary. This is contrary to the conventional model of fields

being propagated in all directions. Thus access to any one region of the

boundary would not allow reconstruction of the contents of the whole

universe. To do that for all particules would require access to the whole

boundary.

Third, Cordus does not support the idea that a single cosmological

boundary completely codes for up-to-date information on every particule

in the universe. It also rejects the idea that ‘All of the possible histories of

the universe, past and future, are encoded on the apparent horizon of the

universe’ [3], and instead suggests that the outer boundary only contains

information about the genesis epoch, with successively concentric inner

boundaries coding for the state of the universe at later times.

Fourth, Cordus does not support the idea that the inner volume of the

universe can be controlled from the outside surface, for reasons more

fully explored below.

6.2 Implications

Can the universe be controlled from outside?

The explicit implication of the conventional idea of the cosmological

horizon is that the inner universe of 3D matter could be controlled from

outside, by an intelligent Agent that could access the outer 2D horizon

[17]. This thought-provoking idea has significant existential implications

for reality. Cordus rejects this as a fanciful notion, for the following

reasons.

First, as already noted, the Agent would need to control the whole entire

horizon simultaneously (as opposed to only one patch). This task is

physically infeasible, given the size of the universe, and the necessary

coordinated control would need to be instantaneous to have any useful

control purpose. This excludes any physical Agent.

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Second, a physical Agent is further excluded because such an Agent,

positioned around the cosmological boundary, would therefore become

part of the process whereby the void is colonised by matter and its fields.

Thus the Agent would become part of the system being measured and

controlled, and the unidirectional causality could not be maintained. It is

therefore not possible, according to the Cordus theory, to have an

independent physical Agent, observer, or inanimate instrumentation at

the boundary.6

The third objection is that there is, according to the Cordus theory, no

bidirectional causality between the 2D surface and the inner 3D volume.

Even if there was a non-physical (metaphysical) Agent at the boundary,

one nonetheless able to meddle with the boundary hyff, a frontier

interaction does nothing to change the emitting particule. This

interpretation arises because the Cordus theory suggests that discrete

fields are unilateral interactions with mono-directional causality. Hyff are

not a conduit for bi-directional force transfer.7 Consequently, the discrete

field pulses that are received at any inspection point remote from the

emitting body are a force on any matter at that inspection point, and have

no reciprocal effect back on the emitting body.

The only way for an Agent on the boundary to change the particules inside

the universe is for the Agent to emit its own discrete fields back into the

universe to target those particules. However this would require a physical

agent (which we already exclude) to generate the discrete fields. This is

because discrete fields are a feature of matter, and do not have an

independent pre-existence. There is a further obstacle too: even if it were

somehow possible to generate discrete fields without matter, these

would take time to arrive at their target, thereby adding a practical

limitation to the efficacy of the control.

So there are three objections to the control idea, the most fundamental of

which is that simply intercepting the discrete fields of the original emitting

6 Elsewhere the Cordus theory shows that the act of observation changes the

system, i.e. observation is necessarily contextual. This applies to photons in

double-slit and interferometer apparatus. In the case of the cosmological

boundary there is a similar principle, except here the addition of the Agent adds

to the system under observation. 7 The idea that forces like gravitation are bidirectional is a tacit assumption in

classical mechanics. The relation for gravitation, F = G ma mb /r2 specifically

identifies that the force depends on both masses, not one. The Cordus theory

accepts this at the macroscopic level, but suggests that the effect is not a

bidirectional force conduit between the two masses, but rather two independent

effects that are aggregated. More specifically, that discrete fields emitted from

source A cause their recipient target B to experience prescribed constraints on

the re-energisation location of its reactive ends, and this is what we perceive as

force. The recipient body B also sends out its own discrete fields, some of which

are intercepted by A, and the mutual attraction/repulsion of the EMG forces

arises by a combination of the individual unilateral effects. Simple passive access

of field information does not necessitate control of the emitting source, according

to the Cordus theory.

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particule is insufficient for controlling that particule. The universe can

therefore not be controlled from its boundary. For all these reasons, the

Cordus model excludes the possibility of placing a physical Agent at the

boundary of the universe, and also shows there is no practical way to

control the universe from the outside. The control aspects of the

holographic principle are therefore rejected. We have not excluded the

possibility that a metaphysical Being may be able to achieve this, but for

such considerations one must look to theology not physics.

Implications for cosmological principle

The Cordus theory proposes that the fabric is approximately

homogeneous and isotropic within the matter compartment of the

universe. However, both those fail in the outer shells where the fabric

density is lower and increasingly directionally. Thus the Cordus theory

proposes that the cosmological principle of homogeneity and isotropy of

the universe is only approximately true, and only for the central part of

the universe. Consequently the concept of comoving distance (distance

between objects, corrected for expansion of the universe), which is based

on the isotropic assumption, also becomes unreliable in the Cordus

theory. Furthermore the Cordus theory for time [9] proposes that there is

no universal cosmological time, and so even proper distance becomes

time-dependent (even without an expanding universe).

Implications for event horizons and black holes

Regarding the implications for the event horizon of a black hole, the

Cordus model acknowledges that it is conceivable to position a physical

Agent outside that horizon (unlike the case of the universe), but asserts

that would still not give any control of the inner workings of the black

hole, for the reasons already given.

What has been achieved?

This paper makes several novel contributions. The first is that it shows

that it is possible for a non-local hidden-variable theory to provide an

interpretation of the cosmological boundary. This is unusual since NLHV

solutions, typified by the de Broglie-Bohm pilot wave theory [18-20], are

focussed on the sub-atomic scale and usually have little to say about

cosmological effects. A second contribution is the provision of an

alternative explanation for the boundary and a dismissal of the control

elements of the holographic principle. The contribution here is not so

much the provision of a more valid competing theory, since neither

explanation can at this time be validated, but rather the provision of new

considerations to enrich the debate. A third contribution is the provision

of a new theoretical model for the composition of the vacuum. This

explanation is integrated with a theory for discrete field elements and

hence also gravitation.

Falsifiable predictions

Making falsifiable predictions about the cosmological boundary is difficult,

since it is inconceivable that anyone could be in that location of space to

put them to the test. Nonetheless there are some subsidiary effects that

are perhaps testable. The main one is the Cordus prediction regarding the

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unilateral causality of gravitation at the smallest scales. According to this

perspective, a body A emits discrete gravitational fields, some of which

are intercepted by remote body B. The Cordus theory predicts that such

an interaction only changes B. The corollary is that B can only change A by

sending discrete fields to A. It is not inconceivable that this might be

testable by using pair-production or annihilation to abruptly bring the two

bodies into/out of existence, and thereby test whether or not the

presence of both is required for the arousal of the gravitation force. While

we have couched this test in terms of gravitation, Cordus predicts the

same should apply to the electrostatic force, and this might be easier to

arrange into an experiment.

Implications for the Cordus conjecture, and future research questions

This paper has provided an explanation for the cosmological boundary.

Since the validity of this is unknown, the result is not suggested to be

evidence confirming the Cordus conjecture. Nonetheless it does expand

the range of phenomena for which the conjecture has an explanation, i.e.

it expands the fitness (as opposed to the validity) of the solution. The

Cordus theory can now offer a logically consistent theory for a wide range

of effects. These include wave-particle duality, Brewsters’ angle, force

unification, asymmetrical baryogenesis, and now some cosmological

implications. That coverage is more extensive than competing theories,

even though some, like QM, have greater detail and quantitative

formulism.

Future research questions along the Cordus line would be the expansion

mechanism and composition of the fabric at the outer boundary. In

particular, it cannot be determined from this model whether the process

of colonising the void is done by the fabric discrete fields, or by outward

motion of massy particules with the fabric following (or both). Also, we

note that the theory requires the void to have a three dimensional

geometry which is ready for colonisation, and so a deeper ontological

question arises of why the void should have a latent three dimensional

structure.

There are many other related cosmological questions, e.g. how time

works, anomalous gravitation (dark matter), accelerating expansion (dark

energy), early inflation, asymmetrical baryogenesis etc. This integration

has not been achieved with either relativity, quantum mechanics, or string

theory. Obviously it is desirable that any theory of physics should explain

all these too. Currently the Cordus theory can explain time, inflation, and

asymmetrical genesis, so there is more work to be done.

7 Conclusions

We have shown that the cosmological frontier has a physical

representation in the Cordus theory. However the principles are

transformed and the implications are different. The Cordus theory

proposes that the outer boundary contains information about the

location of the primal particules at genesis, and the inner shells code for

the changed locations of those particules and any new (or annihilated)

particules since. This conceptual model arises from a consideration of the

17

Cordus theories for the discrete field structure of particules (a NLHV

solution), and the composition of the fabric of the vacuum.

The Cordus boundary model rejects several of the implications of the

conventional holographic models. In particular it suggests that the

universe cannot be controlled from its outer boundary. This is for two

main reasons. The first is the impossibility of locating a physical agent

there to do the controlling. The second is that there is predicted to be no

causality from the boundary of the universe to its inner contents, so

accessing the fields on the boundary would not provide any control of the

particules inside the universe. Also rejected are the notions that the

boundary contains information about both the future and past, or about

all possible universes.

END OF MAIN PAPER [21]

A Appendix: Cordus theory

A.1 Cordus conjecture

What is the Cordus conjecture?

The Cordus conjecture is a non-local hidden-variable (NLHV) solution. It

has been applied to explain entanglement and wave-particle duality [7].

The conjecture starts by questioning the premise of particles being zero-

dimensional (0-D) points [22], then infers what functionality is required,

and then anticipates through design an internal and external structure

sufficient to deliver that functionality. This structure is called the cordus

particule. The term ‘particule’ is used in contrast to the conventional zero-

dimensional ‘particle’. Abandoning the premise of zero-dimensional

particles is a profound conceptual change that unlocks a world of new

solution possibilities. The Cordus conjecture infers the attributes

(functionality, dimensions/variables, properties, causal mechanics) of the

particules in this new framework.

The Cordus theory has been developed by application of system design

principles. The initial concept has been further refined by checking the

theory against a variety of phenomena, and designing new features and

properties on the basis of requisite variability.8 The resulting theory has

8 Design is particularly good at this activity of inferring the necessary internal

structure from the functionality required. In typical applications of new product

development (NPD), the design process is applied to the future functionality, e.g.

the specification desired by a customer. The outcomes of a design process, at

least in NPD, are specifications of the physical geometry, materials, operating

system, and manufacturing structure of an engineered product. Design is

particularly effective at inferring geometry for a requisite functionality, hence

often expressed in drawings, but is capable of defining internal structure in other

ways too, including principles of operation and assembly. There may be more than

one design solution. The design methodology is also valuable when the problem is

18

high fitness to explain many phenomena in physics, within one logically

consistent conceptual framework.

A.2 Cordus particules

Inner structure of the Cordus particule

The basic idea is that every particule has two reactive ends, which are a


interaction with the external environment [23]. A fibril joins the reactive

ends and is a persistent and dynamic structure but does not interact with

matter. It provides instantaneous connectivity and synchronicity between

the two reactive ends. Hence it is a non-local solution: the cordus is

affected by more than the fields at its nominal centre point [24]. The

reactive ends are energised (typically in turn) at a frequency [25].

External structure: Cordus discrete field structures

When the reactive end is energised it emits discrete force elements in up

to three orthogonal directions.9 Within our model we refer to these

discrete force pulses as vires. Although for convenience we use the term

discrete force for these pulses, the Cordus theory requires them to have

specific attributes that are better described as latent discrete prescribed

displacements. This is because a second particule that receives one is

prescribed to energise its reactive end in a location that is slightly

displaced from where it would otherwise position itself. Thus in the

Cordus theory, that which we perceive as force is fundamentally the effect

of discrete prescribed displacements acting on the particules. Force

becomes coercive displacement. See Figure A.1 for examples of the

Cordus structure and principles.

Each reactive end of the particule is energised at the frequency of that

particule (which is dependent on its energy). It emits a discrete force

element (vis, vires: L., ‘force’) when it is energised, and the Cordus theory

requires a continuity between these pulses. Conceptually they are strung

together in a flux line. We refer to this linear structure as a hyperfine-fibril

(hyff). Each reactive end of the particule emits three such orthogonal hyff,

at least in the near-field. These directions are termed hyperfine-fibril

emission directions (HEDs). Particules at close-range interact by

over-constrained or the requirements are conflicting. In these cases it tends to

offer a range of solutions, which differ by the criteria they preferentially satisfy.

One particular design solution may satisfy more of the constraints than other

solutions, and is then considered to have higher fitness. In this case we apply the

design methodology, but the functionality that we seek to support is the observed

behaviours of physics. The outcome we get is a design for the physical features

and operating principles of particles. In other words, if particles were to have

these features then we can explain the (observed) functionality. 9 Nominally the directions are designated radial (r), axial (a), and tangential (t).

This differentiation is useful for the photon, which has a direction of motion,

though less applicable to stationary particules. Earlier papers used the term

‘hyffon’ for the discrete force element (DFE). We have changed the terminology to

avoid the implication that these elements are 0-D particles. The terms ‘vis’

(singular) and ‘vires’ (plural) are Latin for ‘force’.

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negotiating complementary HEDs and synchronising the emission

frequencies of their discrete force elements, and hence bonding arises.

The aggregation of hyff from multiple particules creates a discrete field.

In this theory electric charge is carried at 1/3 charge per hyff, with the sign

of the charge being determined by the direction of the discrete force

element. So the number and nature of energised HEDs determines the

overall electric charge of the particule. For example, the electron is

proposed to have three discrete field elements. Neutral structures are

accommodated, but incompletely filled HEDs are proposed as the reason

for instability [14]. A HED notation has been derived to represent these

proposed discrete force structures [26]. We acknowledge that we have

not described what these discrete field pulses comprise. Instead, the

Cordus conjecture simply shows that having such elements is a logical

necessity for this solution.

The discrete force element is a 3-D composite structure, with a hand

defined by the energisation sequence between the axes. In the Cordus

theory this hand provides the matter/anti-matter species differentiation

[27]. The direct lineal effect of the discrete force element provides the

electrostatic interaction, the bending of the hyff provides magnetism, and

the torsion of the DFE composite provides the gravitation interaction [28-

29]. These are all carried simultaneously by the discrete force element as

it propagates outwards on the hyff line.

20

Figure A.1: Cordus models for the proposed structure of several particules.

The basic structure includes reactive ends, fibril, and discrete force

elements. It is the number and nature of the discrete forces that

determines the externalised behaviour of the particule.

The Cordus theory provides that the discrete field structures (hyff)

around assembled massy particules compete spatially for emission

directions, and may synchronise their emissions to access those spaces.

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Thus there is mutual negotiation in the near-field between interacting

particules, based on shared geometric timing constraints, and this

synchronicity is proposed as the mechanism for the strong force [11].

Thus the Cordus theory provides force unification by providing a model

for electro-magnetic-gravitational-synchronous (EMGS) interactions as

consequences of lineal, bending, torsion, and synchronicity effects

respectively. Consequently the theory rejects the conventional idea of the

Standard Model that every force has a different messenger particle, thus

specifically rejecting the concepts of QM gauge bosons and QCD gluon

colour particles.

In the Cordus theory the photon is required to have a single radial discrete

force element which it periodically extends and withdraws. By comparison

all massy particules have permanent discrete forces that they continue to

generate (at the frequency of the particule) and propagate out into space.

This includes neutral particules like the neutron. The difference in field

structures between the photon and electron, then explains [30] why the

photon generates an evanescent field that decays exponentially whereas

the electrostatic field of electron decays at 1\r2.

A.3 Contrasts

While such a solution may seem precluded by the Bell-type inequalities

[31-32] there is reason to believe those constraints are questionable [33-

34] and we propose that the Cordus model falsifies them [22]. The Cordus

idea goes beyond conventional NLHV solutions, such as the de Broglie-

Bohm model [18], by offering a solution not only for the inner contents of

a particle, the hidden variables, but also predicts how its discrete fields

operate.

The Cordus theory competes with QM, and makes specific assertions of

the deficiencies of QM and the bounds of applicability of that mechanics

[35]. Thus it is proposed that QM is only a statistical approximation to a

deeper and faster phenomenon that it cannot track. Nonetheless Cordus

theory accommodates QM as an adequate approximation for specific

situations. It likewise accommodates elements of general relativity [9].

Furthermore the Cordus theory provides a physically natural explanation

as a counter-point to the abstraction of string theory [36].

A.4 Applications

The Cordus particule theory is characterised by two tightly-integrated

designs. One covers the proposed internal structure of the particule,

specifically the two reactive ends and fibril. The other describes the

discrete force structures and the hyff emission directions (HEDs). These

two designs are linked by the logical necessity for the reactive ends to

emit the discrete fields. The Cordus conjecture shows that if matter and

photons had the proposed structures, then a large number of

fundamental phenomena in physics can be explained within a logically

consistent framework.

It is the conceptual coupling between the discrete fields and the internal

structures that gives the Cordus theory the power to offer explanations to

22

a wide range of phenomena and several enigmatic problems of

fundamental physics and cosmology.

The Cordus theory provides explanations for the following phenomena:

� Collapse of photon to specific location (e.g. double slit and

interferometers) [37] [38].

� Derivation of basic optical laws for reflection and refraction [7].

� Superposition [7] [39].

� Frequency [40] [25].

� Entanglement and the superluminal transport of information [24].

� Electro-magnetic-gravitational fields [28-29] [41-42], Strong force

[43] [11], unification of forces [42].

� Matter particules [41] [43].

� Fabric and vacuum [8].

� Coherence [37] [35], irreversibility and decoherence [35, 44],

entropy [45],

� Superconductors, superfluids and quantum vortices [39].

� Differentiation of matter and antimatter species [27].

� Annihilation process [46].

� Parity violation [12].

� Neutrino behaviour [15].

� Neutron decay [14].

� Pair production and asymmetrical baryogenesis [12].

B Appendix: Lemmas

The following assumptions are built into or emerge from this Cordus

theory, and expressed as lemmas. The lemmas represent the Cordus

mechanics, and are a mechanism to ensure logical consistency within the

theory.

CM-07-03 Fabric hyff Lemma

.1 Each reactive end of the particule, when energised, emits discrete

force element(s) (vis, vires: Latin, ‘force’).

.2 There is only one type of discrete force element (vis) which on its

own is fundamentally electrical in nature, being created by

charged particules.

.3 Electric charge is carried at 1/3 charge per discrete force element

(vis).

.4 The sign of the charge is determined by the direction of the

discrete force element (vis). Outwards is taken as negative (a sign

convention).

.5 The number and nature of energised HEDs determines the overall

electric charge of the particule. Neutral particules arise from

balanced discrete force elements. The opposition here is in

direction, not hand.

.6 For any one particule there is a continuity between these pulses.

Conceptually they are strung together like pulses down a line. We

refer to this linear structure as a hyperfine-fibril (hyff) or flux line.

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.7 Each reactive end of a massy particule emits three such

orthogonal hyff, at least in the near-field. These directions are

called hyperfine-fibril emission directions (HEDs).

.8 The discrete force element is a 3-D composite structure, with a

hand defined by the energisation sequence between the axes. This

hand provides the matter/anti-matter species differentiation.

.9 All of the electric, magnetic, gravitational, and strong

(synchronous) forces (EMGS) are carried by the discrete force

complex. These are all carried simultaneously by the discrete force

element (vires) as it propagates outwards on the hyff flux line.

.9.1 The direct lineal effect of the discrete force element

provides the electrostatic interaction.

.9.2 The bending of the hyff provides magnetism.

.9.3 The torsion of the discrete force composite provides the

gravitation interaction.

.9.4 Particules at close-range interact by negotiating

complementary HEDs and synchronising the emission

frequencies of their discrete fields, and hence strong force

and bonding arises.

.10 The photon has a single radial discrete force element which it

periodically extends and withdraws. By comparison all massy

particules have permanent discrete forces that they continue to

generate (at the frequency of the particule) and propagate out

into space. The photon can alternatively be considered a transient

on the fabric hyff.

.11 The aggregation of discrete force elements in hyff, from many

particules, creates a discrete field.

.12 The fabric of the universe is made of the hyff of all the massy

particules in the observable universe.

.13 The frequency of the particule emitting the discrete force

elements determines the spacing thereof. Therefore the frequency

of the hyff field line varies for different types of particules.

.14 The density of the hyff in the vacuum determines the temporal

capacitance and therefore the propagation speed of light through

the vacuum.

.15 Propagation of light through matter, e.g. glass, involves additional

hyff generated by the matter of the medium. This increases the

hyff density and lowers the speed of light. Hence also refractive

index.

CM-07-06 The cosmological boundary lemmas

.1 Vacuum and Void: The vacuum is that part of the universe and its

surrounds that have a non-zero fabric density. The void is that

region beyond the outer boundary of the cosmos, and is

characterised by having neither fabric nor time.

.2 The cosmological boundary forms where the fabric (vacuum)

expands outwards and colonises the void.

.3 The candidates for composition of the boundary are antineutrinos

produced as a by-product of asymmetrical genesis, and the

discrete force elements (vires) from particules within the universe.

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.4 The discrete forces that make up the fabric propagate outwards

(along the hyff) in increments of one span-length of their

originating particule at each frequency cycle. They can do this in

the absence of other hyff.

.5 The cosmological boundary contains the discrete electro-

magnetic-gravitational (EMG) fields of only the primal particules

within the universe.

.5.1 The coding is only for the particules at the genesis epoch,

not for their present position within the universe nor even

for their ongoing existence.

.6 A shell structure is predicted to develop for the universe, with

intermediate shells containing discrete fields from later epochs of

the universe.

.6.1 Information about changed attributes of particules is

carried out by the hyff at the local speed of light, and

therefore reaches outer shells much later.

.6.2 Any one intermediate shell contains discrete fields from a

range of epochs, since the spatial spread of matter

ensures that some bodies are closer and others further

from any one point on the shell. In the limit this reduces to

an observable universe, i.e. a volume of space which has

had sufficient time to send its discrete fields to the

location under examination.

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